Through an online website. Kayak, Bing, and other sites are helpful in finding flights, especially back to the US.
Through discount airlines. There are several discount airlines, but the best (at least cheapest + most destinations) from Seoul as of mid-2011 are Cebu Pacific and Air Asia. While the first flight will always take you to the Philippines or Kuala Lumpur, respectively, they connect to most destinations in Asia (including but not limited to Singapore, Thailand, Vietnam, etc.) + beyond (Australia, London, etc.) for cheaper than a majority of other options. For a list of discount airlines in Korea, feel free to check out:
Booking Flights
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Places to visit!
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Africa:
Americas:
Europe:
Oceania:
Middle East: